{
  "model": "Heisenberg",
  "lattice": "triangular",
  "n_sites": 900,
  "boundary": "P",
  "params": {},
  "instance_id": "Heisenberg/triangular_900_P",
  "rows": [
    {
      "energy": -1985.5008,
      "sigma": 0.0036,
      "energy_variance": null,
      "dof": 900,
      "einf": 0,
      "v_score": null,
      "method": "ViT",
      "method_detail": "spatial attention, b = 3, translations + C6v projection",
      "method_as_published": "ViT with Spatial Attention, translations + C6v projection",
      "family": "transformer / ViT",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Viteritti, Rende, Sachdev & Carleo, Approaching the Thermodynamic Limit with Neural-Network Quantum States, arXiv:2602.02665",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:2602.02665 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading, parsed from the committed HTML table and matched against the PDF text",
        "reported_as": "-0.551528(1)",
        "note": "Table 1, 30 × 30 block, row 'ViT', printed '-0.551528(1)', 'This work'; caption: 'The results of this work are obtained by enforcing translational and C6v point-group symmetries (refer to Section V.2)'. | Table 1 prints ground-state energies per site of the spin-1/2 triangular Heisenberg model on periodic L x L clusters (Sec. III: 'All calculations are performed on periodic L x L clusters with L chosen as a multiple of 3', H = J sum S_i.S_j), S.S units. Magnitude check: the values lie between -0.5517 and -0.5520, next to the 12 x 12 value -0.55315 (GCNN, per site, S.S) on Heisenberg/triangular_144_P, not four times it (Pauli) or a total.",
        "secondary_of": null
      },
      "compute": {
        "parameters": 450000,
        "gpu_hours": 25000,
        "device": "NVIDIA GH200",
        "n_devices": null,
        "samples": 16384,
        "wall_clock": null,
        "cpu_core_hours": null,
        "bond_dimension": null,
        "iterations": 5600,
        "evaluation": {
          "stages": [
            {
              "iterations": 5000,
              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 1
            },
            {
              "iterations": 500,
              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 9
            },
            {
              "iterations": 100,
              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 108
            }
          ],
          "sr": {
            "kind": "minsr"
          }
        },
        "reported_as": "The Vision Transformer architecture used in this work comprises h = 12 attention heads, n_l = 8 layers, and an embedding dimension of d = 72, resulting in approximately P ≈ 4.5 × 10^5 trainable parameters for different system sizes, from L = 18 to L = 42. [...] we set b = 3 for the triangular lattice [...] (C6v group for the triangular lattice [...]) [...] Variational Monte Carlo (VMC) optimizations employing M = 2^14 samples for the stochastic estimates were carried out using SR with the linear algebra trick being in the regime P ≫ M enhanced with SPRING. The optimization proceeded in three stages: 5000 steps without symmetry summation, followed by 500 steps including translational symmetries, and a final 100 steps with both rotational and reflection symmetries restored. || Acknowledgments: The numerical experiments performed in this work required 25000 hours on GH200 GPUs.",
        "source": "Sec. V B Architecture and Optimization Details; Acknowledgments, arXiv:2602.02665 (mining pass 2026-09-28)",
        "scope": "paper",
        "confidence": "medium",
        "note": "gpu_hours = 25000 is the total for ALL numerical experiments in the paper (triangular L = 18-42 and the 20x20 J1-J2 run), not for this row. parameters 'approximately 4.5 x 10^5', stated for every triangular size. iterations = 5000 + 500 + 100 stated stages; samples = 2^14 per step. Stages: 1 evaluation per amplitude unsymmetrised; b^2 = 9 translations within a 3x3 patch; those 9 x the 12 C6v elements = 108. sr minsr (the P >> M linear-algebra trick with SPRING)."
      }
    },
    {
      "energy": -1986.48,
      "sigma": 0.036,
      "energy_variance": null,
      "dof": 900,
      "einf": 0,
      "v_score": null,
      "method": "ViT",
      "method_detail": "spatial attention, b = 3, variance → 0",
      "method_as_published": "ViT with Spatial Attention, zero-variance extrapolation (triangular)",
      "family": "transformer / ViT",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "Viteritti, Rende, Sachdev & Carleo, Approaching the Thermodynamic Limit with Neural-Network Quantum States, arXiv:2602.02665",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:2602.02665 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading, parsed from the committed HTML table and matched against the PDF text",
        "reported_as": "-0.55180(1)",
        "note": "Table 1, 30 × 30 block, row 'Zero Variance', printed '-0.55180(1)', 'This work'; caption: 'For each system size the zero-variance extrapolated energy is also reported'. Sec. V.3 / Fig. 6: linear fit of energy against variance per site over the unprojected, translation-projected and fully projected ViT states at this L; an extrapolation of the same runs, not a separate calculation. | Table 1 prints ground-state energies per site of the spin-1/2 triangular Heisenberg model on periodic L x L clusters (Sec. III: 'All calculations are performed on periodic L x L clusters with L chosen as a multiple of 3', H = J sum S_i.S_j), S.S units. Magnitude check: the values lie between -0.5517 and -0.5520, next to the 12 x 12 value -0.55315 (GCNN, per site, S.S) on Heisenberg/triangular_144_P, not four times it (Pauli) or a total.",
        "secondary_of": null
      },
      "compute": {
        "parameters": 450000,
        "gpu_hours": 25000,
        "device": "NVIDIA GH200",
        "n_devices": null,
        "samples": 16384,
        "wall_clock": null,
        "cpu_core_hours": null,
        "bond_dimension": null,
        "iterations": 5600,
        "evaluation": {
          "stages": [
            {
              "iterations": 5000,
              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 1
            },
            {
              "iterations": 500,
              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 9
            },
            {
              "iterations": 100,
              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 108
            }
          ],
          "sr": {
            "kind": "minsr"
          }
        },
        "reported_as": "The Vision Transformer architecture used in this work comprises h = 12 attention heads, n_l = 8 layers, and an embedding dimension of d = 72, resulting in approximately P ≈ 4.5 × 10^5 trainable parameters for different system sizes, from L = 18 to L = 42. [...] we set b = 3 for the triangular lattice [...] (C6v group for the triangular lattice [...]) [...] Variational Monte Carlo (VMC) optimizations employing M = 2^14 samples for the stochastic estimates were carried out using SR with the linear algebra trick being in the regime P ≫ M enhanced with SPRING. The optimization proceeded in three stages: 5000 steps without symmetry summation, followed by 500 steps including translational symmetries, and a final 100 steps with both rotational and reflection symmetries restored. || Acknowledgments: The numerical experiments performed in this work required 25000 hours on GH200 GPUs.",
        "source": "Sec. V B Architecture and Optimization Details; Acknowledgments, arXiv:2602.02665 (mining pass 2026-09-28)",
        "scope": "paper",
        "confidence": "medium",
        "note": "gpu_hours = 25000 is the total for ALL numerical experiments in the paper (triangular L = 18-42 and the 20x20 J1-J2 run), not for this row. parameters 'approximately 4.5 x 10^5', stated for every triangular size. iterations = 5000 + 500 + 100 stated stages; samples = 2^14 per step. Stages: 1 evaluation per amplitude unsymmetrised; b^2 = 9 translations within a 3x3 patch; those 9 x the 12 C6v elements = 108. sr minsr (the P >> M linear-algebra trick with SPRING). This row is the zero-variance extrapolation of the same three stages (Fig. 6), not a separate run, so it draws the same cost again."
      }
    },
    {
      "energy": -1963.2528,
      "sigma": null,
      "energy_variance": null,
      "dof": 900,
      "einf": 0,
      "v_score": null,
      "method": "VMC",
      "method_detail": "Jastrow-Gutzwiller",
      "method_as_published": "Jastrow-Gutzwiller",
      "family": "classic VMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Ghorbani, Tocchio & Becca, Variational wave functions for the S = 1/2 Heisenberg model on the anisotropic triangular lattice: Spin liquids and spiral orders, Phys. Rev. B 93, 085111 (2016), arXiv:1512.03356 (quoted in arXiv:2602.02665)",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "secondary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:2602.02665 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading of the quote; primary read, value not located",
        "reported_as": "−0.545348",
        "note": "Table 1 of arXiv:2602.02665, 30 × 30 block, row 'Jastrow-Gutzwiller', printed '−0.545348' with no error bar, attributed to [71] = Ghorbani, Tocchio & Becca 2016. Not located in the committed text of arXiv:1512.03356 (searched '0.5453', '30×30', '900', 'extrapolat'; its Tables I-II are 18 × 18 only): may come from a later version, a figure, or the authors directly. No sigma stored, none printed. | Table 1 of arXiv:2602.02665 prints energies per site of the triangular Heisenberg model on periodic L x L clusters, S.S units.",
        "secondary_of": "arXiv:2602.02665"
      }
    },
    {
      "energy": -1972.56176758,
      "sigma": 0.160722,
      "energy_variance": 258.31409,
      "dof": 900,
      "einf": 0,
      "v_score": 0.059748826873951125,
      "method": "2D RNN",
      "method_detail": "iterative retraining, s = 4.0, r = 0.158",
      "method_as_published": "2D RNN wavefunction (iterative retraining, s=4.0, r=0.158)",
      "family": "RNN",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Moss, Wiersema, Hibat-Allah, Carrasquilla & Melko, arXiv:2505.20406v3 (2025-10-13)",
      "peer_reviewed": false,
      "source": "repo-data-2026-09-28",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "authors' data release read locally (pickle via numpy), values copied by key, no transcription; the file is committed as sources/2505.20406-repo-final_energies_data.json and reproduces Table V's L = 6 energy and Table II's V-scores",
        "reported_as": "-0.5479338243272569 +/- 0.000044644868135991976 per site (S.S), Var(E/N) = 0.00001993164250880112, V-score 0.05974882616027808",
        "note": "github.com/mschuylermoss/HeisenbergRNN, commit 5f5cffa5cb (2025-10-28, HEAD; file last changed in d58a945cd4 2025-05-27, 'final plotting data and plotting notebooks'), Triangular/final_plotting/plotting_data/final_energies_data_plotting.pkl, sha256 bdc59e5bc3780fb4ea7444400dc9abd9984a6a259ab03f9299c1f80edb87d276: ['TriangularMS,periodicBC']['scale=4.0,rate=0.158,T=1.00'], L = 30. The paper's most accurate schedule (Table II, whose L = 30 V-score 6.0e-2 is this run's 0.0597); plotted in Fig. 4(a), not printed; quoted as -0.54793(1) in Table 1 of arXiv:2602.02665, whose error bar is not the primary's. TriangularMS is the 120-degree basis rotation U_tri, which changes the representation, not the Hamiltonian. Variance is Var(H)/N^2 in S.S units; total = var x N^2 x 16.",
        "secondary_of": null
      },
      "compute": {
        "parameters": null,
        "gpu_hours": 1700,
        "device": "NVIDIA H200",
        "n_devices": 2,
        "samples": 10000,
        "wall_clock": null,
        "cpu_core_hours": null,
        "bond_dimension": null,
        "iterations": null,
        "reported_as": "Sec. IV Discussion: The longest simulation reported in this work took 1,700 GPU hours and produced energies for six different system sizes up to 30x30, albeit with more modern hardware (see Appendix E). Appendix E, Figs. 10-11 captions: ... using two H200 GPUs. Fig. 4 caption: Each of our variational energies is estimated with 10x10^3 samples.",
        "source": "Sec. IV Discussion, Appendix E Figs. 10-11 captions, Fig. 4 caption, arXiv:2505.20406 (compute pass 2026-09-16, block reused for the repository row)",
        "scope": "ansatz",
        "confidence": "medium",
        "note": "1,700 GPU-hours is the paper's total for its longest iterative-retraining chain (L = 6 ... 30), read as the s = 4.0, r = 0.158 schedule this row comes from; the paper does not split it per size. No parameter count stated."
      }
    }
  ],
  "url": "https://qmbl.org/i/Heisenberg/triangular_900_P/",
  "per_site_divisor": 3600,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -1985.5008,
    "sigma": 0.0036,
    "method": "ViT",
    "method_detail": "spatial attention, b = 3, translations + C6v projection",
    "reference": "Viteritti, Rende, Sachdev & Carleo, Approaching the Thermodynamic Limit with Neural-Network Quantum States, arXiv:2602.02665",
    "bound_type": "variational",
    "energy_per_site": -0.551528
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  "no_record_reason": null
}